Editing Elementary algebra (section)

=== Linear equations with one variable ===
{{Main|Linear equation}}

Linear equations are so-called, because when they are plotted, they describe a straight line. The simplest equations to solve are [[linear equation]]s that have only one variable. They contain only constant numbers and a single variable without an exponent. As an example, consider:

: Problem in words: If you double the age of a child and add 4, the resulting answer is 12. How old is the child?

:Equivalent equation: <math>2x + 4 = 12</math> where  {{mvar|x}} represent the child's age

To solve this kind of equation, the technique is add, subtract, multiply, or divide both sides of the equation by the same number in order to isolate the variable on one side of the equation.  Once the variable is isolated, the other side of the equation is the value of the variable.<ref>{{Cite book|title=All the Math You'll Ever Need|author=Slavin, Steve|publisher=[[John Wiley & Sons]]|year=1989|isbn=0-471-50636-2|page=[https://archive.org/details/allmathyoullever00slav/page/72 72]|url=https://archive.org/details/allmathyoullever00slav/page/72}}</ref> This problem and its solution are as follows:
[[File:Divide large.gif|alt=|thumb|Solving for x]]
{|
|-
| 1. Equation to solve:
| <math>2x + 4 = 12</math>
|-
| 2. Subtract 4 from both sides:
| <math>2x + 4 - 4 = 12 - 4</math>
|-
| 3. This simplifies to:
| <math>2x = 8</math>
|-
| 4. Divide both sides by 2:
| <math>\frac{2x}{2} = \frac{8}{2}</math>
|-
| 5. This simplifies to the solution:
| <math>x = 4</math>
|}
In words: the child is 4 years old.

The general form of a linear equation with one variable, can be written as: <math>ax+b=c</math>

Following the same procedure (i.e. subtract {{mvar|b}} from both sides, and then divide by {{mvar|a}}), the general solution is given by <math>x=\frac{c-b}{a}</math>